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Physics of MRI 8: Advanced Concepts - Part 2
Physics of MRI 8: Advanced Concepts - Part 2
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Hey my name is Marshall Sussman, I'm an MRI physicist at the University Health Network and University of Toronto. I've been giving a series of lectures on basic MR physics. And this lecturer is gonna be the second part of advanced concepts in MRI. In the first part of this lecture we went through the concepts of spectroscopy, MR safety and SSFP. In this part of the lecture I'm gonna focus on parallel imaging, diffusion and propeller. So let's start out

with parallel imaging. So what is it? It's just simply a method for reducing the amount of data we need to acquire in order to generate an image. And there's a number of different techniques related to parallel imaging that have different names depending on the vendor and depending on the specific implementations, so some examples smash, sense, asset and the list can go on. So why

is it that you wanna reduce the amount of data that you need to acquire?. Well the reason is because it reduces the overall scan time. So just to give you an example of that, let's say we start up with a convectional acquisition, where we're gonna require a complete set of k-space data. Now, what if we require only every second line of k-space rather than the full

accent of k-space. So we reduce the amount of data we need to acquire, and what's the effect of that? Well we know that in convectional imaging if we simply did that, the field of view is inversely proportional to the space scene of our case base samples. So if we increase the space in between our k-space samples, that means our field of view's going to be reduced. And in general, so if for example

if we dropped every other line of case base, we'll drop our field of view down by half. And we know from the artifacts lecture that in general that's going to lead to aliasing, the field of view gets to be smaller than the anatomy or imaging. So just as an example of that, here we have an image of the brain, and if we had a very small field of view, then we would get aliasing. So obviously

that's gonna be unacceptable if the anatomy we're interested in, lies in the alias region. So with parallel imaging this is essentially a mathematical method that allows us to remove the aliasing. So we could get an image that essentially, completely removes the imaging using parallel imaging. So again, what's the advantage? So it's to reduce scan time. So let's just say, for

example, that it takes five milliseconds to acquire a line of k-space. So the overall scan time is gonna be equal to, five milliseconds times the number of lines we have to acquire. So if we have only half as many lines we need to acquire, then we're gonna reduce our overall scan time by half. So you can see this week, it allows for a significant take, savings in scan time. Now depending on

the parallel imaging technique you use, it's possible to eliminate more than one line of k-space. And in general, the number of lines you eliminate. is called the acceleration factor. So if I eliminate, say every other line of k-space, I have an acceleration factor of two, if I eliminate three lines of k-space, then I'm going to have an acceleration factor of three.

what's the limit? In general the acceleration factor has to be less the number of coil elements. So if I have for example 16 coil elements in my multi channel coil, and I can only image up to a maximum acceleration factor of 15. In practice the limit is often significantly less than that so this is sort of a maximum theoretical limit. So what are the disadvantages of parallel imaging? Well, first

of all signal to noise ratio. So we know that signal to noise ratio is proportional of the square root of scan time. So if we reduce the scan time, then that reduces the SNR. So that essentially a penalty that's inherent to any imaging technique which images faster. So the shorter the scan time, the lower the SNR. However, in the case of parallel imaging, there's an additional parallel imaging specific

penalty. And this is called the G-factor penalty. So this is an additional SNR penalty on top of the one that we take that's associated with reduction of scan time. So just to give an example of that, here I have three images of the brain, acquired with an increase in acceleration factor so two, three and four. So what you can appreciate is that, as we increase

the acceleration factor, in other words as we reduce the scan time, the signal to noise ratio, decreases. So that's expected because again we reduce our scan time, lessen our proportional scan time, so we reduce our scan time or SNR decreases. However, scan time penalty, should be uniform across the image so we should expect a uniform SNR penalty. But you can appreciate most prominently

in the acceleration factor equal to four, that the signal to noise ratio actually varies non uniformly across the image. And that non uniform loss, is the additional loss associated with this G-factor penalty. So you can appreciate that we have again specific penalty of parallel imaging with SNR as well as the more general penalty of the reduced scan time. Well also, another disadvantage of parallel

imaging is that in some cases there can be some artifacts that are specifically associated with parallel imaging. If the reconstruction doesn't end properly or if the setup isn't correct, then this can lead to some specific artifacts associated with parallel imaging. Now as I mentioned there's a number of different flavors of parallel imaging,

two of the sort of the earliest ones and the most widely cited one are smash and sense and these just are variations on the way that the data is dealt with, so smash operates on case based data while sense operates on the image data and there's many different versions of this, some that hybridize various different components of this, and many different flavors of parallel imaging. Next we're

gonna move on and talk about diffusion weighted imaging. So diffusion imaging is a technique in MRI, that generates contrast between tissues based on the microscopic motion of water. In other words based on differences in the microscopic motion of water. So in general water that can move freely around or is very mobile, tends to have a different signal and diffusion images than water

that's so called restricted or has much more difficulty in moving around. So for example, syrup which is much thicker will have a different signal than water would on a diffusion weighted image. So what is the pulse frequency used for diffusion weighted imaging? So the basic pulse sequence is shown here and this is somewhat of a simplification that illustrates the basic concepts. So as we've

shown many times in the past, we have our initial RF pulse that tips on magnetization and you can see we have our x and y gradients in our data acquisition, which actually includes the image, so this is essentially the imaging part which you've seen many times before. But in diffusion wave imaging, there's an additional component added prior to imaging and this is the part that actually encodes the

diffusion encoding. And there's different ways of doing this but the one I've shown you here, is a pair of opposite polarity gradients or positve and negative gradient that we apply before we then capture the information in our imaging components of the pulse sequence. So what do those offset polarity gradients do? Why do they encode motion? So let's consider the case where we have a molecule that

initially lies at the position that you see here. And let's also assume that we've turned on a gradient like you see in the image above. So we know from our basic MR physics, that because the molecule sees a certain magnetic field it's gonna rotate at a particular frequency, so over time the [INAUDIBLE]

associate with the water molecule will rotate. So that's the positive polarity gradient. If we then turn on the negative polarity gradient, so the magnetic field that it sees, is now much smaller so it's gonna then rotate in the opposite direction. So if we turn on that gradient for the exact same amount of time as we turn on the positive polar ingredient and after a period of time, magnetization will

go back to its original position. So in this case the net effect of this gradient, of these two opposite polarity gradients, will be essentially nothing to the phase of that molecule. So now let's consider a second situation, where we turn on this positive polarity gradient, but in this case, let's consider what happens when the molecule is moving. So initially,

let's say we turn on the gradient, and the magnetization associated with that molecule, again accumulates phase. Let's now assume that this water molecule, moves to a different position. Okay, we then turn on our gradient of the opposite polarity. So again, now, the molecule sees a different magnetic field strength. However, it's not exactly the same one, as we saw in the first case. It's

not the opposite of the one we saw in the first case. So it will rotate in the opposite direction, but we'll do so at a different frequency. So after a period of time, after you've played out this opposite polarity gradient, it won't re-phase back to exactly the same position, because again, it's experienced one gradient of one amplitude on the positive

polarity, and it's experiencing a different gradient when we have a different magnetic field on the negative polarity. Now, if that instead molecule instead will move to that position had moved to a third position, then again the magnetic filed that it will see, will be again different. So, depending on where that molecule moves to, that will determine what sort of magnetic field it will see.

And that will determine how much it's actually re-phased. So if it sees that it hasn't moved and it see exactly the same magnetic filed then it will be perfectly re-phased. If it sees a larger difference in magnetic field, in other words if it moves more, it will have a of less complete re-phasing, so in general, after the diffusion encoding part of our pulse sequence the water molecules will have

a phase that will depend on the amount of diffusion so if things diffuse faster, we'll have a different phase with things that diffuse slower, or things that are stationery and it's that difference in phase which is what we're encoding in the diffusion coding component of the pulse sequence. So up to now we've been talking about diffusion effects on an individual

water molecule, but now let's step back a little bit and look what happens over a region of tissue when we have a large number of water molecules. So in general, here's one water molecule, there's another one, and in general we'll have many water molecules distributed throughout the tissue. Now, due to diffusion, the water molecule will de-phase relative to each other because each water molecule

will experience a slightly different motion, because of course it's a random Brownian type of motion. But depending on how quickly these water molecules are moving around, will depend on the spread of different motions that are seen and this will in turn affect the amount of dephasing. So the amount of dephasing that we have will then in turn directly be proportional to the signal loss.

So for example, if we have water molecules that are completely immobile, then they'll all have the same phase as a result of that of that gradient, those two gradients of opposite polarity. If molecules are moving on very very rapidly relative to each other, then there'll be a large number of different phases after we play out those two opposite polar ingredients, so have a greater distribution of phase

and therefore a greater signal loss. In general again the more freely water can move around, the greater the distribution of phases after we play out the two opposite polar gradients and the greater the signal loss. So the more diffusion, the greater is the signal loss on following diffusion in coating. So up till now, I've shown you how in tissues where water can move around more freely, we'll

tend to get a larger signal loss upon diffusion encoding however there's also additional factors will lead to the pulse sequence itself it can also affect the signal loss. So in particular, properties related to the diffusion encoding ingredients, will have a strong effect on the amount of signal loss we have, in particular the strength, length

and separation between our two diffusion cord ingredients, will the amount of signal loss is related to something called the B-value. So this is just a parameter that takes into account those three different factors I just mentioned. So I won't go into the mathematical derivation of it, I'm just gonna present the result for you as

you see below. Showing you that the B-value is the factor that determines the amount of signal loss based on the pulse sequence parameters. Mathematically, again, I won't go through the derivation I'll just present the result, we saw that the signal loss, varies exponentially as a function of the B-value. So the same loss we get is E minus B, which is the B value times something called the

apparent diffusion coefficient. So the apparent diffusion coefficient is related to have freely water can move around. So this is very similar to what we've encountered before with T2 decay. So T2 decay call was also an extension signal loss but In that case we had T, the parameters T and T2 rather than the B and the diffusion coefficient. So in this case, the B value correspond

to time so in expense to T2 decay it says time went on, the amount of exponential decay increased, in this case as the B values increase, we get a larger amount of signal decay. In this case, the apparent diffusion coefficient, corresponds to one over the T2 value so again apparent diffusion coefficient just relates to how freely water can move around, the more freely water can move around, the larger

the apparent diffusion coefficient. So again as I mentioned earlier, things with the larger apparent diffusion coefficient means water can move more freely and therefore that leads to a larger signal decay. Now, just like in T2 imaging, where we get T2 wave of contrast we can also get a diffusion wave of contrast. So in particular let's say we have a tissue that has a different apparent diffusion coefficient,

then if we image with a particular B value, we can generate a diffusion wave of contrast. So this is just the same as we generated T2 way of contrast by choosing a particular echo time, so to generate a diffusion way to contrast we choose a particular B value, that correspondingly generates a contrast based on differences in the apparent diffusion

coefficient. So in general, the larger the B value we use, the heavier the diffusion wave of contrast in other words the more of a difference in signal we can get between tissues with different apparent diffusion coefficients. So this is similar to the TE parameter and T2 way to the machines so in that case the larger the TE value, the heavier the T2 wave of contrast. So here, we have an example that illustrated

here where we use a larger B value we get a larger difference in signal between the two tissues with different diffusion coefficients. However, one thing that should be pointed out, is the larger the B value, in general the lower the overall SNR so we can see that the contrast between two different Issues increases but the overall SNR of both of the tissues decreases.

So in general if we use too large of a B value, while we may get a large contrast between the tissues, the overall signal will be too low to actually use it to generate a meaningful image. So diffusion wave imaging has many different applications. One of the most successful is as an indicator of acute stroke. So in the brains of people who've had an acute stroke. Because pain on the diffusion would lead to

coefficient that is a very strong detector of the presence of particular types of strokes and I'll show you an example that you see in the image that I'm presenting here. [BLANK_AUDIO] Now, one thing that you can appreciate from the description I had given you up to this point, is that we turned on gradients in the

y direction, and what that allowed us to do, is encode motion that occurs in the y direction of the same direction as the gradient. However, we can also encode diffusion information other directions as well. So for example, if we turned on a series of opposite clarity gradients in the x direction, and that would encode diffusion information in the x

direction. And in general, you can imagine that these may not be the same. so for example let's say we have a nerve fiber, you can imagine that the water can move more freely along the direction of the neural fiber rather than in the perpendicular direction or the cross sectional direction. So you can imagine that water, the apparent diffusion coefficient, would be different in the two different

directions of fibers. We can actually extend this concept to essentially map out the direction of diffusion and we can generate what I call fiber tracts or tractography images of the brain. So here's a nice example of that, it shows you images of the fiber tracts in the brain, based on again the direction of water diffusion. You can also see the same sort of thing in other tissues, here we have

an example of tracking fibers in the calf muscle. So this now is supposed to tracking neural fibers as in the previous case, this is now tracking muscle fibers. And again, using the same sort of diffusion encoded type of information. Last topic we're gonna discus today is related to propeller. So I'm gonna walk through the basic pulse sequence underlying propeller.

So let's say of here we have our case based data set, so in propeller, just as in all the previous case-based acquisition strategies we've gone through in detail before, require a series of lines of case phase just like you see here. So if this was a normal gradient echo type pulse sequence, we would just continue this until we acquire the full extent of k-space. however, the key concept in color

is that we only acquire limited set of k-space date, or case phase lines. We than next we rotate those lines, and reacquire them. So we rotate which lines of k-space we're then gonna be acquiring. And we continue doing that process one after another, and you could see why this is called propeller, because the regions of case phase require and essentially

rotate like the blades of a propeller. Once we do that, for a specified number of times, we can then fill up the entire extent of case phase that we need to generate. So you can see that from the middle image here. Now, notice with this sort of approach, we're essentially over sampling regions in k-space. So for example the region at the center, we basically acquire on every single blade of the

propeller, where as the outer regions when we only acquire on one or a few blades of the propeller. After we acquire the full extent of k-space as per usual we acquire apply for a transform and this generates the resulting image that you see on the far right. [SOUND] Now, as I mentioned, with this approach, we're essentially over-sampling the center of k-space. On every single acquisition, every single

bleed of this propeller, we're repeatedly acquiring the center of k-space. Now what happens if we reconstruct an image just from the center of k-space? Well, recall from our earlier k-space talk, if we reconstruct images from the center of k-space that will give us essentially a low resolution image of the anatomy like you see on the image

on the right table. So on every single blade of the propeller, we can form a low resolution image of the anatomy. Now that's actually used to correct for motion. Because, let's say motion is occurring on subsequent acquisitions of each of the propellers like you see in the image that I've shown you here. So on the first image we have the brain in the central position,

we move to acquire the second however, you can see the brain has moved up, and a third blade propeller, the brain has moved down to a lower right-hand corner. So whenever you blade the propeller, the anatomy itself has being moving around. Now if we were to just simply reconstruct the image at this point without taking any further action, obviously we would have motion

artifacts, because the data would be inconsistent from the different blades of the propeller. However, the key in the propeller is that since we can form a low resolution image on each of the blades, we can detect the motion and ultimately correct for it. So we can correct individually each blade of the propeller before we combine the data together, and we can then eliminate or minimize the amount

of artifacts we have in our resulting image. So once you apply a transform to the corrected image, we were gonna get an image that's free of artifacts. So just to summarize, so with the power we can correct for both translations and rotations in the image. So that's the major advantage underlying propeller, so it corrects for motion. There are a couple of disadvantages

however. So first of all, in general propeller scans take longer than a corresponding rectilinear case-based acquisition equivalent. And the reason is again cuz we're oversampling portions of case fails, so for oversampling in general that's gonna take longer. 50% increase in scan time is not unheard of using a propeller

approach. The other disadvantage of propeller is there's no defined phase and frequency in code direction. So because we're rotating the blade of the propeller we can't say, with the horizontal direction is phasing code, vertical direction is frequency in code, because in general phasing frequency code direction will change on every acquisition. So this can lead to a number of drawbacks with respect

to floor artifacts and also aliasing artifacts. So for example in case of an aliasing, there's no one dimension that will be free of aliasing artifacts. If you recall one of the tricks we played with our rectilinear acquisitions, we like to place the long dimension of the anatomy in the frequency encode direction because aliasing doesn't occur in the frequency-encode direction. We can't use that

trick with propeller, because there is no single frequency encode direction. So in general aliasing will occur at all the positions of the anatomy if our field of view is smaller than the anatomy. Here, we just have an example of propellers. So the image on the left, was just acquired with just a conventional fast spin echo pulse sequence, so this is just a convectional rectilinear

acquisition and the image on the right was acquired with propeller. So both of these images were acquired when the patient was in motion. And you can see in a conventional fast spin echo image we have severe motion artifacts, whereas in the case of propeller We've essentially eliminated virtually all of these artifacts. So this is really the main advantage

of propeller and this is one of the major reasons why it's coming quite utilized in patients scans. So that brings us to the end of the second part of the advanced concepts in MRI lecture, thank you for listening and I hope you'll join me

for the subsequent lectures. Thank you. [BLANK_AUDIO]

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